anritsu - vna poster 01-2014

Circuits and Waves

+

Vg Vi

Zo

ZL

Ii

(1)

(2)

ai

bi

Vi + Zo Ii

Zo

ai

bi-

+ =

-1

(3) vi (ai + bi)Zo =

(4) li (ai - bi)Zo

=Vi - Zo Ii

Zo 2

2

=

Figure (1) Relation between waves and terminal voltage and current

Reflection coefficient i at port i, where the terminating impedance ZL = Vi/Ii

(5) (6) (7) Return Loss (dB) at port i:

Inserting equation (6) into equation (1) and squaring it yields (8)

Where PGA is available power from the voltage source Vg

The power incident minus the power reflected is given by:

(9)

Where: PL = power delivered to load PR = reflected power

When Z0 = ZL then L = 0 and all of the power is transfered to the load and (10)

The scattering parameters describe the relationship of a set of variables called ai and bi, the incident and reflected waves at the ith port of a microwave network. These waves are defined in terms of the terminal voltage Vi and terminal current Ii with an arbitrary real impedance Z0 (see Figure (1)).

S-Parameters

a1DUT

s21

s22s11s12

b2

b1=

b2

s11

s21

s12

s22

a1

a2

b1 a2

bg

gL

Signal Flow Graphics for input and output

+

VibLZL

aL

aL igigbg

bs

vgVg

bL

aL

aLbL =

bL

iL

vL

-

+

-

+

-

Circuit Representationfor load

Signal Flow GraphRepresentation Circuit diagram for voltage

sourceSignal flow diagram

The nodes represent incident (a) or reflected (b) power waves

Source voltage = Vg

Source impedance = Zg

Characteristic impedance of transmission line Zo

Load impedance ZL

L gL=

L

ZL - ZoZL + Zo

L=Vg

Zg + Zoig = bg = + agg

a

Zo=

Zg bg

ag

Zg + Zo=

Zo Vgg = Zg + Zo

Zg - Zo=

Figure (2) Input and output signal flow graph representations

Figure (3) Signal Flow graphs used for 2-Port Network

1 Mason, Samuel J. (July 1956). Feedback Theory - Further Properties of Singal Flow Graphs. Proceedings of the IRE: 920-926

The square matrix [S] represents the relationship between the vectors [a] and [b] that represents the amplitude and phase of the incident and reflected waves.

Where:

(12) S11 = b1/a1 forward 1 at port (1) when the load reflection coefficient (L = 0) and a2 = 0

(13) S21 = b2/a1 transmission coefficient from port 1 to port 2 when (L = 0) a2 = 0, matched load on port 2

(14) S12 = b1/a2 reverse transmission coefficient from port 2 to port 1 when (G = 0) a1 = 0, matched source on port 1

(15) S22 = b2/a2 reverse 2 at port (2) when the reflection coefficient (g = 0) and a1 = 0

The signal flow graphs can be generally solved for the reflection coefficient ii = bi/ai and transmission function Tij = bj/ai using Masons Rule

1.Signal flow graphs are an excellent method to analyze microwave circuits. The S-Matrix and the source are represent-ed by the graph shown in Figure (3)

The definition of the Scattering Matrix [S] is given by:

(11) [b]=[S][a]

In microwave circuit design S-parameters are useful for characterization of any 2-Port network. S-parameters are determined using a reference impedance usually equal to the characteristic of the test system (generally 50 ohms).

The S-parameters are complex elements having a magnitude and phase, and are measured in term of incident and reflected waves (a and b) using a Vector Network Analyzer (VNA).

Vi Vg ZoIi=

=RL 20Log10| i|

Vi Vg ZoIi=

=RL 20Log10| i|

1

____________________________________________________

Start section 1

Circuits and Pseudo Power Waves

The scattering parameters describe the relationship of a set of variables called pseudo power waves (ai and bi), the

incident and reflected power waves at the ith port of a microwave network are defined in terms of the terminal

voltage Vi and terminal current Ii with an arbitrary real impedance Z0 (see figure( 1)).

Zo

Vg

+

-bi

ZL

-

+

Vi

Ii

ai 1( ) ai

ViZoIi

+

2 Zo

= 3( ) Vi

Zoai

bi

+( )=

2( ) bi

ViZoIi

2 Zo

= 4( ) Ii

1

Zoai

bi

( )=

.Figure (1) Relation between Pseudo Power Waves and terminal voltage and current

Power wave refection coefficient at port i, where the terminating impedance ZL=Vi/Ii

==

! !

=!!

(6) =

Return Loss (dB) at port i:

(7) = ||

Inserting equation (6) into equation (1) yields || =

||

=

Where is available power from the voltage source Vg


(8) ||

=

= =

Where: PL=power delivered to load

PR=reflected power

When Zo=ZL then GL=0 and all of the power is transferred to the load and

i

PGA

1

____________________________________________________

Start section 1





Zo

Vg

+

-bi

ZL

-

+

Vi

Ii

ai 1( ) ai

ViZoIi

+

2 Zo

= 3( ) Vi

Zoai

bi

+( )=

2( ) bi

ViZoIi

2 Zo

= 4( ) Ii

1

Zoai

bi

( )=



==

! !

=!!

(6) =


(7) = ||


||

=



(8) ||

=

= =


PR=reflected power


i

PGA

1

____________________________________________________

Start section 1





Zo

Vg

+

-bi

ZL

-

+

Vi

Ii

ai 1( ) ai

ViZoIi

+

2 Zo

= 3( ) Vi

Zoai

bi

+( )=

2( ) bi

ViZoIi

2 Zo

= 4( ) Ii

1

Zoai

bi

( )=



==

! !

=!!

(6) =


(7) = ||


||

=



(8) ||

=

= =


PR=reflected power


i

PGA

2

(9) PL=|| =

End section 1

Start section 2

S-Parameters

The definition of the Scattering Matrix [S] is given by:

(10) [b]=[S][a]

In microwave circuit design S-parameters are useful for characterization of any 2-Port network. S-

parameters are determined using a reference impedance usually equal to the characteristic of the test

system (generally 50 ohms).

The S-parameters are complex elements having a magnitude and phase, and are measured in term of

incident and reflected waves (a and b) using a Vector Network Analyzer VNA.

Signal Flow Graphs for input and output

Source voltage = Vg

Source Impedance = Zg

Load Impedance ZL

g

bs

bg

ag

ZL

+

-

vL

aL

bL

iL aL

bL

L

Zg+

-

es vg

ig

+

-

LbL

aLThe nodes represent incident (a) or reflected (b) power waves

bL L aL

Circuit Representation for load

Signal Flow Graphrepresentation

Circuit diagram for voltagesource

Signal flow diagram

igVg

Zg Zo+

a

Zobg

Zo es

Zg Zo+ag g+

Figure (2) Input and output signal flow graph representations

g L

bg a1

b1

b2

a2

S11

S21

S22

S12

b1

b2

S11

S21

S12

S22

a1

a2

=

DUT

Figure (3) Signal Flow Graphs used for 2-Port Network

bg = Zg + Zo

Zo Vg Vg g = Zg + Zo

Zg - Zog =bg =

(Zg = Zo)(Zg = Zo)(0)2

Zo

Reflection Coefficient

180 0

90

-90

G

0

-5

-10

-15

-20

-25

-30

-35

Mag

nitu

de (d

B)

Return Loss (Mag)

Frequency (GHz)5 10 15 20

Smith ChartFrom equation (5), we haven

50:

Inductive Reactance

Capacitive Reactance

OpenShort

Complex Impedance Z = R+ jX

Figure (5) |S11| plotted as RL = 20*log10|S11|

Figure (4) Polar Display of Reflection Coefficient G

Figure (6) Smith Chart DisplayCircles are constant resistance (R),

Arcs are constant reactance (X)

The magnitude fot the reflection coefficient |S11| is graphically represented as a Return Loss (equation 7) and plotted as the log magnitude versus frequency as shown in Figure (5).

The reflection coefficient is graphically represented as a polar display (shown in Figure 4). For passive systems the magnitude of is 1. From equation (5), we have equation (16).

We have a 1 to 1 relationship between and Z().For example: when ZL = Z0 = 0, for an open or short circuit then || = 1.The VNA maps the impedance space into the polar display of as a Smith Chart shown in Figures (7 and 8). For every corresponding point in space, there is a corresponding impedance ZL. The VNA measures the reflection coefficient and plots the impedance ZL.The Smith Chart is the bi-linear trasnformation of the reflection coefficient space to the impedance Z space.

ZL 1+1-ZO

=( )

Phase and Group Delay

Phase Delay

Figure (7) Phase delay with frequency of a DUT usinglinear format

Figure (8) Residual phase variation after removal oflinear term

16n

14n

12n

10n

8n

6n

4n

2n

0

-2n

-4nCh1 TR Start 38.7 GHz Stop 39.5 GHz IFBW 100 Hz Avg OFF Measuring State CORR

Tr1 S21 Trans Grp Dly RefLvl: 0 s Res: 2 ns/Div

M1 : 39.415 GHz 9.7903 ns> M2 : 38.82 GHz 8.7577 ns

21

Group Delay

Figure (9) Group delay of a Band-Pass filter showingconstant group delay in the Band-Pass and the

distortion at the band edges.

Phase delay (the argument of the Sparameters) is usually displayed in a linear phase format as a function of frequency Figure (7). This display shows the measurement from 180 to +180 degrees. This display method keeps the display discon-tinuity removed from the important 0 degree area which is used as the phase reference.The linear phase delay can be unwrapped (removal of the linear term) leaving only the deviation from linearity as shown in Figure (8).There are several ways in which all the information can be displayed on one trace. One method is a polar display as shown in Figure (4). In this display, the radial parameter |S| is magnitude, while the rotation around the circle is phase. Polar displays are used to view transmission measurements, especially on cascaded devices.

The S21 parameter describes the transmission charateristics of the DUT.The argument 21 of the S21 represents the phase delay of the signal as it progates through the DUT. The group delay defined by the Brillouin equation

(17) is the propagation group delay through the DUT.

The VNA uses the approximation The smaller the frequency step () the better the approxima-tion. The plot of the group delay for a filter is shown in Figure (9).

VNA Architecture

Figure (10) Block diagram for dual band VectorStar VNA

50 GHz

70 GHzFrequency

SRD

NLTL

Tran

sfer

Fun

ctio

n

Figure (11) Comparison of the performanceof NLTL sampler to harmonic mixing

The dual band VectorStar VNA is comprised of a mixer based low band (70 KHz to 2.5 GHz) VNA using bridge reflectome-ter and a high band (>2.5 GHz) using NLTL samplers and broad band coupler reflectometer. This design allows the VNA to operate at very low frequencies for superior time domain measurements.

For the high band (>2.5 GHz) the VNA uses four Non Linear Transmission Line (NLTL) sampler receivers and associated reflectometers to measure a1, a2, b1, and b2 waves incident and reflected from the DUT. The ratios for each of the S-Param-eters are calculated using data measured at each sampler. Because S-parameters are ratios, it is not necessary for the samplers to measure absolute values. For example, when measuring S11, it is only necessary to know the level at b1 relative to a1. Figure 10 shows the block diagram for the VNA. Under normal test conditions, the input of the DUT would be attached to port 1 on the VNA, and the output of the DUT would be attached to port 2.

Notice from the block diagram that samplers a1 and a2 meas-ure the power from the source via a power splitter. Samplers b1 and b2 measure the response at both port 1 and port 2 via couplers at the respective ports. A normal calibration corrects for the input and output couplers, as well as any external cabling associated with a measurement setup.

The NLTL sampler receivers have very wide inherent bandwidth (>150 GHz). The instantaneous bandwidth of the IF can be as high as 200 MHz for wide band pulse measurements when using a broad band A/D converter.

The NLTL harmonic sampler receivers offer higher dynamic range and lower conversion loss that the Step Recovery Diode (SRD) samplers and fundamental mixers whose transfer function tends to drop off by about 50 GHz as shown in the Figure (11). The NLTL technology offers higher frequency performance >150 GHz before the first null. This results in excellent dynamic range: >100 dB to 110 GHz with excellent stability.

Sampler a1 measures the incident signal onto the DUT (when port 1 drives)

Sampler a2 measures the incident signal onto the DUT (whenport 2 drives)

Sampler b1 measures the reflected signal back from the DUT(when port 1 drives)

Sampler b2 measures the transmitted signal at the output of the DUT (when port 2 drives)

Optional

a1 a2

b1 b2

a1

b1 b2

Port 1 Port 2

> 2.5 GHzHigh Band A

< 2.5 GHzHigh Band A

B

DUT

a2

Bias 1 Bias 2

Superposition/True Mode Stimulus

True-differentialmode (180 degrees

out-of-phase)

True-differentialmode (180 degrees

out-of-phase)

SweptPhase

+ +

Common-mode (in phase) inputand common-mode outputIn Out1

Common-mode (in phase) inputand differential (180 degreesout of phase) output

2

Differential inputand common modeoutput

3

Differential input anddifferential output4

5 6

In Out

In Out

In Out

50

40

30

20

10

0

-10

-20

-30

-40

-50Ch1 TR Start 0 Stop 360 IFBW 100 Hz Avg OFF Measuring State UNCORR

Tr2 SDD(1:2) LoqM RefLvl: 0 dB Res: 10 dB/Div

Figure (14) 4-port balanced measurement system

The stimulus input to the DUT and possible output measurements are shown below in Figure (15)

Testing Balanced Devices using Superposition or True Mode Stimulus Using a VNAVector network analyzers are capable of using superposition to determine the characteristics of differential passive or linear active DUTs. Each side of the differential device is stimulated in turn and the results combined mathematically. However, for non-linear differential devices, this method does not work and it is necessary to stimulate both sides simultaneously using dual sources and true mode stimulus capability. The VectorStar VNA does this using its internal second source and DifferentialView options.

Testing balanced devices using DifferentialView Apply true mode stimulus to differential balanced devices in a four-port mode (two ports for input and two for output) The differential sources are amplitude and phase adjusted to get the match-corrected signal relationship or equal amplitude and 180 phase difference at the DUT reference planes All balanced parameters are fully error-corrected

Figure (15) The new basis for analyzing mixed-mode S-parameters is shown here. With the physical ports considered as pairs, one

can analyze in terms of common-mode and differential drive and common-mode and differential output.

Figure (16) An example phase sweep measurement isshown here of the differential return loss (SDD) of a

balun-based front-end. The match null is centered near 180 degrees as one would expect and is realtively broad.

Measure device performance in an unbalanced state Set amplitude or phase to an offset relationship Sweep phase to determine device performance and find device anomalies

The measurements set-up is shown in Figure (14)

Pulse Measurements

MasterSamplingClock

T0 Markers010001000100

Pulse Generator

Processor

TOT0 in

T0 out

ADC a1 Data010001000100

ADC b1 Data010001000100

ADC a2 Data010001000100

ADC b2 Data010001000100

IF Channels

Figure (12) The data acquisition systemin the MS4640B series with High Speed

IF Digitizer

10

0

-10

-20

-30

-40

-50

-60

-70

-80

-90Ch1 PROF 0 s 400 ns [CW] 10 GHz IFBW 10 MHz Avg 10/10 Measuring State UNCORR

Tr1 S21 Trans LoqM RefLvl: 0 dB Res: 10 dB/Div

Figure (13) The pulse magnitude S21 response for an amplifier

Pulse MeasurementsThe Anritsu VectorStar VNA offers the option of the use of a wide band high speed (14 bit > 400 mega-sample) digitizer processor and specific pulse software to acquire and display pulsed signals.

To understand the operation of the pulse acquisition system of the Anritsu MS4640B the IF channel for each receiver is shown in Figure (12).

The VNA IF signals are generated by the non-pulse down converters in the MS4640B. When equipped with pulse mode option the standard IF system is bypassed and signals are routed to a special high-speed digitizing IF board. This board consists of analog processing (filtering, gain, calibration) with a much wider bandwidth than the standard IF system, which enables the measurement of much narrower pulses. This board also houses the fast analog-to-digital converters, pulse generators, and digital processing components. Deep memory (4GB) is used to store the data coming in from the converters. As a result, the Anritsu MS4640B can acquire long time records of more than 0.5 seconds with full resolution. The magnitude of S21 for a pulsed amplifier as function of time is shown in Figure (13).

Component Step Response Impulse Response

G = 1, Open

G = 1, Short

Resistor, r > Z

Resistor, r < Z

Inductor

Capacitor

Figure (17) Example of Time Domain responses

Time Domain

The rise time of a DUT is calculated using: =

Low-Pass ProcessingThe basic capability of the VNA is to measure in the frequency domain the signals of S-parameters of an RF or microwave device and display the result.

The Fourier transform provides a method for transforming VNA frequency domain data into the time domain mode. Low-Pass processing (harmonic frequency measurement) provides twice the spatial resolution of the Band-Pass processing. The DC term must be approximated by extra-polation and harmonic calibration is required. The shape of the real part of the step and impulse response in the Time Domain mode will show the nature of the com-plex discontinuity similar to that obtained by using classi-cal Step Response measurement.

Harmonic frequency VNA data set is required:

(18) F(n) = n*FL, where n =1, 2,...N and N = FH/FL

Band-Pass ProcessingThis processing is idealfor a measurement where the DC term is not available and only discontinuity location is required. VNA data frequency set:

(19) F(n) = FL + n(FH-FL)/N, where n = 0,1,2,3..N

Alias Free RangeFor both the Low-Pass and Band-Pass processing, the inherent alias free time range is:

(20) = (N-1)/(Frequency Span)

For example, with a 40 GHz frequency span and 1,001 data points, the Alias Free Range is: 1000/40 GHz = 25 nanoseconds

Time Domain DisplaysLow Pass and Band Pass processing can identify the characteristics of the reflection coefficient from the real part of the S11(t) display for known components. Rise Time measurements using the VNA

These measurements require the use of Time Domain Transmission, S21(t) Step response. The effective rise time for a VNA is: (VNA) = 1/(FH - FL) where FH is the highest measurement frequency and FL is the lowest measurement frequency. The VectorStar 110 GHz VNA has na effective rise time (the time between the 10% and the 90% magnitude points) of approximately 8.25 pico-seconds measured using a through line.

Relative to Unity Reference

SWRReflectionCoefficient

ReturnLoss (dB)

dB BelowReference Ref +X (dB) Ref X (dB) Ref X (dB)

17.3910 0.8913 1 18.7242 0.7943 2 25.8480 0.7079 3 34.4194 0.6310 4 43 5698 0.5623 5 53.0095 0.5012 6 62.6146 0.4467 7 72.3229 0.3981 8 82.0999 0.3548 9 91.9250 0.3162 10 101.7849 0.2818 11 111.6709 0.2512 12 121.5769 0.2239 13 131.4985 0.1995 14 141.4326 0.1778 15 151.3767 0.1585 16 161.3290 0.1413 17 171.2880 0.1259 18 181.2528 0.1122 19 191.2222 0.1000 20 201.1957 0.0891 21 211.1726 0.0794 22 221.1524 0.0708 23 231.1347 0.0631 24 241.1192 0.0562 25 251.1055 0.0501 26 261.0935 0.0447 27 271.0829 0.0398 28 281.0736 0.0355 29 291.0653 0.0316 30 301.0580 0.0282 31 311.0515 0.0251 32 321.0458 0.0224 33 331.0407 0.0200 34 341.0362 0.0178 35 351.0322 0.0158 36 361.0287 0.0141 37 371.0255 0.0126 38 381.0227 0.0112 39 391.0202 0.0100 40 401.0180 0.0089 41 411.0160 0.0079 42 421.0143 0.0071 43 431.0127 0.0063 44 441.0113 0.0056 45 451.0101 0.0050 46 461.0090 0.0045 47 471.0080 0.0040 48 481.0071 0.0035 49 491.0063 0.0032 50 501.0057 0.0028 51 511.0050 0.0025 52 521.0045 0.0022 53 531.0040 0.0020 54 541.0036 0.0018 55 551.0032 0.0016 56 561.0028 0.0014 57 571.0025 0.0013 58 581.0022 0.0011 59 591.0020 0.0010 60 60

5.53505.07804.64954.24893.87553.52873.20752.91082.63762.38662.15671.94651.75471.58021.42161.27781.14761.02990.92370.82790.74160.66390.59410.53140.47520.42480.37980.33910.30280.27040.24140.21550.19230.17160.15310.13660.12180.10870.09690.08640.07710.06870.06130.05460.04870.04340.03870.03450.03080.02740.02440.02180.01940.01730.01540.01380.01230.01090.00970.0087

19.271513.736510.69078.65857.17736.04125.14054.40963.80633.30182.87562.51262.20131.93311.70071.49881.32271.16871.03370.91510.81080.71890.63780.56610.50270.44660.39690.35290.31380.27910.24830.22100.19670.17510.15580.13880.12360.11000.09800.08730.07780.06930.06170.05500.04900.04360.03890.03460.03090.02750.02450.02180.01950.01730.01550.01380.01230.01090.00980.0087

24.806518.814515.340212.907311.05289.56998.34807.32046.44395.68845.03224.45903.95613.51333.12242.77662.47032.19861.95741.74301.55241.38281.23191.09750.97790.87140.77650.69190.61660.54950.48970.43650.38900.34670.30900.27530.24540.21870.19490.17370.15480.13800.12300.10960.09770.08710.07760.06920.06160.05490.04900.04360.03890.03470.03090.02750.02450.02190.01950.0174

Reflection Coefficient Table

X(Ref+X)

(Ref-X)(Ref )

Phasor Interaction

The first three columns are conversion tables for return loss, reflection coefficient and SWR.

The last four columns are values for interactions of a small phasor X with a large phasor (unity reference) expressed in dB related to reference.

The RF Measurement Chart can be used to deter-mine the uncertatinty due to bridge/autotester VNA directivity. TheX dB Below Reference column represents the difference between the directivity and the measured reflection (return loss). The ref + X dB and ref - X dB values are the algebraic sum of the error signal and the measured reflected signal as their phase relationship varies over 360. Therefore, the peak-to-peak ripple (1 X) is the totalmeasurement uncertainty caused by the error signal.

For example, if a 30 dB return loss is measured witha 40 dB directivity autotester, the X dB Below Refe-rence Value is 10 dB. Ref + X dB is 2.3866 dB and ref - X dB is 3.3018 dB. The actual return loss is between 27.6134 dB (-30 + 2.3866) and 33.3018 dB (-30 - 3.3018). The peak-to-peak ripple on a swept measurement will be 5.6884 dB. If the error and directivity signals are equal, ref + X dB equals 6 dB(voltage doubled causes 6 dB change) and ref - X dB becomes infinite, since the two signals are equal in amplitude and 180 outof phase (zero voltage).

VNA Fundamentals: Look closely, See clearly...

MS4640B 2-port measurements - Enhanced features for component design, radar applications and materials measurements

ME7838A 2- and 4-port 70 kHz to 125 GHz broadband measurements - smallest frequency extension modules for on-wafer device characterization applications and antennas measurements

MS4640B 4-port solutions - New capabilities for signal integrity and components design applications

Nonlinear Transmission LinesHigh frequency VNAs make use of harmonic samplers, or mixers, to downconvert measurement signals to intermediate frequencies (IF) before digitizing them. Such components play a critical role in VNAs, because they set the bounds on important parameters like conversion efficiency, receiver compression, isolation between measurement channels and spurious generation at the ports of a device under test.

Mixers tend to be the down converter of choice in the RF domain, due to mainly to their simpler local oscillator (LO) drive system and enhanced spur management advantages. Nowadays and with Anritsu technology it is possible to employ NLTL based harmonic sampling from RF to microwave and even millimeter wave frequencies.

A nonlinear transmission line (NLTL) is comprised of a transmission line periodically loaded with varactors, where the capacitance nonlinearity arises from the variable depletion layer width, which depends both on the DC bias voltage and on the AC voltage of the propagating wave. An equivalent circuit model of one section of an NLTL is shown in the slide.

NLTLs have successfully been used to generate ultrashort electrical pulses and transients from a sinusoidal input signal. At large signal levels, waveform steepening occurs for the proper choice of input waveform and soliton generation can be achieved by balancing steepening and dispersion. Due to observable compression of the signal slope a NLTL is also often called Shock Line. In the frequency domain this pulse compression results from the generation of a large number of harmonics with suitable phase relationship. The output of such Shock Line is providing a very broadband harmonic rich spectrum of equidistant spectral lines. The closest line to our signal under test is used for the above mentioned harmonic sampling.

More detailed information about Anritsu NLTL and harmonic mixer application can be found in the article: A matter of scale, April, 10th 2012, Karam Noujeim, Jon Martens and Tom Roberts

www.anritsu.com

Whatever your application, Anritsus VectorStar VNA helps you see clearly

anritsu - vna poster 01-2014

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